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A337993
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Numbers k such that L(k) < sigma(k) + k/Pi^2, where L(k) = floor(H(k) + exp(H(k)) * log(H(k))) and H(k) = Sum_{j=1..k} 1/j.
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1
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1, 2, 4, 6, 12, 24, 60, 120, 360, 2520, 5040
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OFFSET
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1,2
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COMMENTS
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Conjecture: This sequence is finite.
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REFERENCES
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S. Ramanujan, Highly composite numbers, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962.
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LINKS
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FORMULA
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MATHEMATICA
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A337993Q[n_] := With[{h = HarmonicNumber[n]}, Floor[h + Exp[h]*Log[h]] < DivisorSigma[1, n] + n/Pi^2];
Select[Range[5040], A337993Q] (* Paolo Xausa, Feb 01 2024 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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